If the stock hits that barrier, though, they will lose half of their investment. That diversification should help reduce the risks of the trade, bankers say. Then, as now, local investors wanted products promising chunkier returns than the measly yields available in bond markets. But in one important difference to that time, banks in the present day are no longer creating pools of equity-default swaps to slice up into an equity market version of complex synthetic collateralised debt obligations.
Hence an Asset Swap has an implicit hedge against a rise in interest rates, as we noted in the Impact Analysis study above. We performed sweeps with the bankruptcy mode off and also with the bankruptcy mode on. The graphs are shown in Figures 1 through 28 below. The graphs are shown in Figures 29 through 36 below. Bankruptcy Mode Off. We discuss the case of bankruptcy mode on below, after first analyzing the results for the case of bankruptcy mode off. If an Asset Swap is valued by setting the credit spread of the underlying bond equal to the ASW recall spread, then we have found that the median life of the Asset Swap is zero.
The advantage of entering into an Asset Swap is based on the expectation of the future credit spreads, behavior of the volatility and interest rates etc. For the purposes of comparison of the bond and Asset Swap metrics, we valued the AMGN bond with a credit spread of bps. We swept the stock price, volatility, credit spread and interest rates. In all the graphs, the dark blue curve describes the bond and the pink curve describes the Asset Swap. We analyze the comparison of the metrics below. Stock Sweep.
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The graphs obtained by sweeping the stock price are the most informative of the various sweeps. As expected, they both have a smoothed out hockey stick shape. This is consistent with the market expectation that holding an Asset Swap requires a smaller hedge than holding a bond. At this stock price level, the median life of the Asset Swap decreases to zero, and so the Gamma of the Asset Swap equals that of the bond. The curves are parallel, but Rho is positive for the Asset Swap and negative for the bond.
The curve for the bond is negative. The curve for the Asset Swap is almost zero, indicative of the fact that the Asset Swap holder has divested himself of the credit risk of the issuer. Roughly speaking, the pure bond part of the convertible has a positive Theta accretion to par , and the option part has a negative Theta.
The Asset Swap holder has only the option part. Effectively, the Asset Swap holder has removed the exposure to the credit risk of the issuer, but at the price of more negative time decay. At such high values of S, the sensitivity to credit spread is very small, and the expected value of the cash flows including the value of the option embedded in the bond make it preferable to hold the convertible.
Volatility Sweep. The graphs obtained by sweeping the volatility are mostly featureless, and are included for completeness of the presentation. The median life of the Asset Swap displays a complicated dependence on the volatility, but it is difficult to draw any conclusions from this fact. Credit Spread Sweep. The graphs obtained by sweeping the credit spread illustrate one fairly obvious point. In all the plots, the curve for the Asset Swap becomes flat as the credit spread is increased.
This is consistent with our expectation that, at high spreads, the bond value declines and contributes little to the valuation of the Asset Swap. Think of a deep out of the money option. The Asset Swap which is valued on a risk-free basis is then insensitive to the precise value of the credit spread, leading to flat curves in the plots. Interest Rate Shift. Unlike a sweep of the credit spread, an interest rate shift changes the risk-free interest rate. This affects the recall value of the Asset Swap, whereas a change in the credit spread does not.
The curves for the Asset Swap therefore do not flatten out as the risk-free rate increases. The graph of the Asset Swap stub and bond fair value is the most informative. Since the Asset Swap has a positive Rho and the bond has a negative Rho , the ASW stub value and the bond fair value move in opposite directions as the risk-free rate increases.
Bankruptcy Mode On. We now discuss the case of bankruptcy mode on. The parameters are the same as in Table 3. We swept only the stock price. We know that when the bankruptcy mode is on, at low parity the fair value of the bond drops to zero, the bond Delta increases in principle to infinity at zero parity , and the Gamma is negative. However, the Asset Swap stub value has a floor of zero and the Delta and Gamma behave more like those of an equity call option, i.
Delta increases from 0 and in an S-curve as the stock price increases, and Gamma is always positive. Hence we expect a significant difference in the graphs of the bond and the Asset Swap. This is confirmed in Figures 29 through 36 below. In all the graphs, the dark blue curve again describes the bond and the pink curve describes the Asset Swap.
The interesting behavior is when the Asset Swap median life is nonzero, i. As the parity decreases to zero, the holder of an Asset Swap would decrease the stock hedge to zero, whereas a bondholder would need to increase the stock hedge. Furthermore, the bondholder would be hurt by the negative Gamma, but an Asset Swap holder does not have this problem. Furthermore, even in the region where both the bond and Asset Swap have positive Gamma e.
The graph for Rho Figure 33 indicates that the Asset Swap continues to have an implicit hedge against a rise in interest rates, and the graph for Theta Figure 35 indicates that the Asset Swap continues to have more negative time decay than the underlying bond. Switching on the bankruptcy mode does not change these aspects of the behavior of an Asset Swap. The graphs for the AMGN Asset Swap and bond, with the bankruptcy mode on, are similar but the differences are not as pronounced.
Basically, with the bankruptcy mode on, if the median life of the Asset Swap is nonzero, then the Asset Swap has a substantially larger Gamma than the underlying convertible, as well as a smaller Delta which goes to zero whereas the bond Delta goes to infinity at zero parity. No excess capital. Invest excess capital at risk-free rate. Interest Rates Rise bps. Interest Rates Fall bps.
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Bond Price. ASW Recall Value. Stock Price.
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Credit Spread bps. Yield Curve. Borrow Cost. Dividend Model. The strategy was originally conceived to exploit mispricing between the implied volatility of the convertible arbitrage position and the listed equity options, or historical realised volatility. In practice, a convertible arbitrage position is truly dynamic in that a number of different exposures can be replicated depending on where the underlying equity trades relative to the conversion price call option strike of the bond.
At lower conversion values, the position exhibits more bond-like qualities, with higher credit sensitivity. Conversely, at higher conversion values, positions have more equity option-like characteristics and higher equity price volatility sensitivity. In addition, managers today may overlay various hedging or directional strategies, including: interest-rate hedges; credit hedges credit default swap or straight bond ; selling the equivalent listed call option to capture a volatility differential ; and adjusting the delta hedge to take more or less equity exposure.
Three factors have contributed to the decline in convertible bond arbitrage in the past decade, in our view: a reduction in leverage; continual decline of a hedged implementation; and decreasing primary issuance. In , the leverage applied to the long side of convertible arbitrage positions approached eight times underlying capital Figure 3. Given the delta-neutral arbitrage implementation, short stock positions were also proportionally inflated.
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When credit facilities from banks were unceremoniously terminated, calamity ensued. Bonds traded below their conversion value, while prime brokers called for liquidation of client accounts. Fast forward to and long side leverage is down substantially to roughly two to three times underlying capital, with the size of the short stock position therefore being proportionally reduced.
Third, the rate of primary convertible issuance has been declining over the past 10 years. By and large, most of the decline can be attributed to issuers opting for high-yield debt in lieu of convertibles; high-yield and leveraged loan markets have grown significantly since , while the convertible market stagnated Figure 5.
A number of factors can be attributed to the deterioration in convertible issuance, including: the diminished coupon advantage of convertibles in a zero-rate world; low implied volatility level higher volatility allow issuers to command greater premiums ; and the ceaseless passive and active strategy demand for vanilla fixed income products over the past decade. This year through 9 September, issuance at USD Note: values to 31 July.